Question

A hamster runs at a speed of 17 centimeters per second in a wheel of radius 10 centimeters​

Answer 1

`16.2\ (rev)/(min)`

Explanation:

The complete question is

A hamster runs at 17 centimeters per second in a wheel of radius 10 centimeters how fast will the wheel spin in revolutions per minute​?

step 1

Find the circumference of the wheel

The circumference of the circle is equal to

`C=2\pi r`

we have

`r=10\ cm`

substitute

`C=2\pi (10)\\C=20\pi\ cm`

assume

`\pi=3.14`

`C=20(3.14)=62.8\ cm`

step 2

Find the number of revolutions

Remember that

One revolution of the wheel represent a distance equal to the circumference of the wheel

using proportion

`(1)/(62.8)\ (rev)/(cm)=(x)/(17)\ (rev)/(cm)\\\\x=17/62.8\\\\x=0.27\ rev`

so

The number of revolutions per second is
`0.27\ (rev)/(sec)`

step 3

Convert to rev per minute

we know that

`1\ min=60\ sec`

to convert sec to min divide by 60

so

`0.27\ (rev)/(sec)=0.27:(1)/(60)=16.2\ (rev)/(min)`